Write the equation that satisfies the given conditions. The line passes through the two points (3, -1) and (-2, 5). Choices A. 5y = 6x - 23 B. y=-6/5x +13/5 C. y = 4x - 13

Answers

Answer 1

(3,-1)(-2,5)
slope = (5 - (-1) / (-2 - 3) = -6/5

y = mx + b
slope(m) = -6/5
(3,-1)...x = 3 and y = -1
sub and find b, the y int
-1 = -6/5(3) + b
-1 = -18/5 + b
-1 + 18/5 = b
-5/5 + 18/5 = b
13/5 = b

so ur equation is : y = -6/5x + 13/5

Answer 2

Final answer:

To find the linear equation of a line passing through two given points, use the formula for the slope of a line to calculate the slope, then substitute this value, along with one of the given points, into the point-slope form of a line and solve for y.

Explanation:

The subject of this question is the formulation of a linear equation, specifically a equation of a line passing through two given points (3, -1) and (-2, 5). The formula used to find the slope (m) of a line between two points is: m = (y2 - y1) / (x2 - x1). Use this formula to calculate the slope using these points(m = (5 - (-1)) / (-2 - 3) = -6/5) .

Next, using the point-slope form of a line, y - y1 = m(x - x1), we substitute m with the calculated slope, and (x1, y1) with one of the given points. (Let's use (3, -1), y - (-1) = -6/5(x - 3) simplifying this gives us the answer: y=-6/5x +13/5. Therefore, the correct answer is choice B: y=-6/5x +13/5.

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Related Questions

You have a rectangular vegetable garden in your backyard that measures 15 feet by 10 feet. You want to double the area of the garden by adding the same distance x to the length and width of the garden. Find the value of x and the new dimensions of the garden.

Answers

Final answer:

To double the area of the rectangular vegetable garden, we need to add the same distance, x, to the length and width. The value of x is 10 feet, and the new dimensions of the garden are 25 feet by 20 feet.

Explanation:

To double the area of the garden, we need to add the same distance, x, to both the length and width of the garden. The original dimensions of the garden are 15 feet by 10 feet, with an area of 150 square feet. To double the area, we set up the equation 2(15+x)(10+x) = 2(15)(10). Solving this equation gives us the value of x and the new dimensions of the garden.

Expanding the equation, we have 30x + x² + 300 = 300. This simplifies to x² + 30x - 300 = 0. Factoring this quadratic equation, we get (x - 10)(x + 30) = 0. So x = -30 or x = 10. We discard the negative value since distance cannot be negative, so x = 10 feet.

The new dimensions of the garden are 15+10 = 25 feet and 10+10 = 20 feet.

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Given: M is the midpoint of LN; LM =8 prove:LN=16

Answers

A midpoint divides a segment into two congruent segments.

If LM = 8, then MN = 8.

Adding both together, you would get 16 for the length of LN.

The proof of LN= 16 is shown below:

What is midpoint?

The midpoint formula is applied when one is required to find the exact center point between two defined points. So for a line segment, use this formula to calculate the point that bisects a line segment defined by the two points.

Given:

LM= 8

and M is the midpoint of LN

So, the line LN will be break into two equal parts LM and MN

then we can write

LM= MN= 8

Now,

LN= LM+ MN

LN= 8+8

L=16

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A rectangle has one side on the xx-axis and two vertices on the curve y=74+x2. y=74+x2. find the vertices of the rectangle with maximum area.

Answers

Given that a rectangle has one side on the x-axis and two vertices on the curve [tex]y= \frac{7}{4+x^2} [/tex]

We find the vertices of the rectangle with maximum area as follows:

Because of the symmetry of the given curve, the base of the retangle is 2x and the height of the rectangle is y.

Thus, the area of the required rectangle is 2xy where [tex]y= \frac{7}{4+x^2} [/tex]

Thus, [tex]Area=\frac{14x}{4+x^2}[/tex]

For maximum area, we find value of x for which the derivative of the function for the area is equal to zero.

The derivative of the function for the area is given by:

[tex](Area)'= \frac{14(4-x^2)}{(4+x^2)^2} =0 \\ \\ \Rightarrow4-x^2=0 \\ \\ \Rightarrow x^2=4 \\ \\ \Rightarrow x=\sqrt{4}=2[/tex]

Thus, the area is maximum when x = -2 and x = 2

When x = -2,

[tex]y= \frac{7}{4+(-2)^2}= \frac{7}{4+4} = \frac{7}{8} [/tex]

Similarly, when x = 2,

[tex]y= \frac{7}{4+(2)^2}= \frac{7}{4+4} = \frac{7}{8} [/tex]

Therefore, the required vertices are: [tex](-2,0),\ \left(-2, \frac{7}{8} \right), \ \left(2, \frac{7}{8}\right), \ (2, 0)[/tex]

Final answer:

The rectangle with maximum area does not exist as the curve y = 74 + x^2 does not intersect the x-axis.

Explanation:

To find the vertices of the rectangle with maximum area, we need to find the points of intersection between the curve y = 74 + x^2 and the x-axis.

Setting y = 0, we can solve the equation 74 + x^2 = 0 to find the x-coordinates of the vertices.

Since the curve is a parabola facing upwards, there are no points of intersection with the x-axis.

Therefore, the rectangle does not exist.

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The length of a rectangle is 4.2 cm more than 2 times the width. If the perimeter of the rectangle is 42.6 cm, what are its dimensions?

Answers

Perimeter= add all

42.6 = 6w + 8.4

34.2 = 6w

w = 5.7

L= 15.6

Factor the four-term polynomial.
xz + x + yz + y
A. (z - y)(x + 1)
B.(x - y)(z + 1)
C.(x + y)(z + 1)

Answers

group like terms , factor out common variable.

(xz+x) + (yz+y)
x(z+1) + y(z+1)

factor out (z+1)

= (z+1)(x+y)
= solution C.

A master electrician earns $62 per hour. His apprentice earns $40 per hour. The master electrician works 3 hours more than the apprentice. If together they are paid $492, how much does the master electrician earn?
A) $292
B) $312
C) $332
D) $372

Answers

Let x be the number of hours the master electrician works and y the numbers of hours his apprentice works.

The master electrician earns $62 per hour, which means that he earns 62x.
His apprentice earns $40 per hour, which means that he earns 40y.

Together they are paid $492, so we can get the equation:
62x + 40y = 492.

We know that the electrician worked 3 hours more than his apprentice. So he worked x = y + 3 hours. Now let's replace x by its new value in the previous equation.

62x + 40y = 492
62(y+3) + 40y = 492
62y + 186 + 40y = 492

Now we need to put variables apart and numbers apart, so we subtract 186 from both sides of the equation:
62y + 40y + 186 - 186 = 492 - 186
102y = 306

Now we divide both sides by 102
(102y)/102 = 306/102
y = 3

So the apprentice worked 3 hours.
As we already mentioned, the electrician worked 3 hours more than his apprentice.
So he worked x = y + 3 = 3+3 = 6 hours.

The master electrician earns $62 per hour. Since he worked 6 hours, he earns 62 * 6 = 372 dollars.

So the master electrician earns $372 (Option D)

Hope this helps! :)

Answer:

The answer is D)$372

Step-by-step explanation:

HELP PLEASE ASAP!
BRAINLIESTTTTTTTTTTTTT

Answers

Can you make it more zoom? Sry i can't see well

Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes Who has more money, Anna or Jasmine? How much more? Explain

Answers

Anna has more money... We don't have to do messy calculations for this... Both have 10 to the 2nd power "some amount". 10 to the second power is 100. So they both have 100 coins.

A quarter is 25 cents, while a dime is only 10 cents. Since they both have the same amounts of coins, the one with 100 quarters has more money, so Anna has more money than Jasmine.

Now, we need to figure put by how much! 100 quarters is one hundred 25 cent coins. 100*25 = 2500. That is 25 dollars. Whereas, Jasmine has one hundred times 10 cents, which is 1000 cents. This is 10 dollars.

So, Anna has 15 more dollars than Jasmine.

This question is based on the concept of logical reasoning.Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.

Given:

Anna has 10 to the 2nd power quarters. Jazmin has 10 to the second power dimes.

We need to calculate the who has more money, Anna or Jasmine.

According to the question,

Anna has 10 to the 2nd power quarters.

In mathematically expressed as,

[tex]\bold{10^2 = 100}[/tex] quarters

Now, Jazmin has 10 to the second power dimes.

In mathematically expressed as,

[tex]\bold{10^2 = 100}[/tex] dimes

So,they both have 100 coins. But, we know that quarter is 25 cents, while a dime is only 10 cents.

Anna has 100 quarters = [tex]\bold{100 \times 25 = 2500}[/tex]. That is 25 dollars.

Jasmine has 100 dimes = [tex]\bold{100 \times 10 = 1000}[/tex]. This is 10 dollars.

Therefore,they both have the same amounts of coins, the one with 100 quarters has more money.Thus, Anna has more money than Jasmine.

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When the federal reserve wants more money to be printed, which agency will be in charge of printing it?

Answers

The U.S. Treasury would be in charge of printing it :)

Answer:

The U.S. Treasury.

Step-by-step explanation:

Kendall is stacking boxes that are 7.5inches tall. Explain how to find the height (in inches)

Answers

You can find the height by finding out the number of boxes and plugging it into an equation. Height = 7.5(Number of Boxes)

Final answer:

To find the height of stacked boxes, multiply the height of one box (7.5 inches) by the total number of boxes stacked.

Explanation:

Kendall is stacking boxes that are each 7.5 inches tall. To find the total height in inches of the stacked boxes, you would need to multiply the height of one box by the total number of boxes stacked. For example, if Kendall stacks 10 boxes, the calculation would be 7.5 inches x 10, which equals 75 inches. Therefore, the total height of the 10 stacked boxes would be 75 inches.

The coordinates of point D are (7, 4) and the coordinates of point E are (1, −3) .

What is the slope of the line that is perpendicular to DE¯¯¯¯¯?

Enter your answer as a simplified fraction in the box.

Answers

ANSWER

[tex]- \frac{6}{7} [/tex]

EXPLANATION

The given points are

[tex](x_1,y_1)=(7,4)[/tex]
and

[tex](x_2,y_2)=(1,-3)[/tex]

The formula for finding the slope is given by,

[tex]slope = \frac{y_1-y_1}{x_1-x_1} [/tex]

We substitute the points to obtain,

[tex]slope = \frac{ - 3 - 4}{1 - 7} = \frac{7}{6} [/tex]

The slope of the line that is perpendicular to DE is the negative reciprocal of

[tex]\frac{7}{6} [/tex]

Thus, the line perpendicular to DE has slope,

[tex] \frac{ - 1}{ \frac{ 7}{6} } =-\frac{6}{7} [/tex]

Write the solution to the given inequality in interval notation.

[-3,-1)
(-3,-1]
(-∞,-3) U [-1,∞)
(-∞,-3] U (-1,∞)

Answers

D, open ( and closed ]

Answer:

D. [tex](-\infty,-3]\text{U}(-1,\infty)[/tex]

Step-by-step explanation:

We have been given solution of an inequality on number line. We are asked to write the solution to the given inequality in interval notation.

We can see that all values of x less than or equal [tex]-3[/tex] and greater than [tex]-1[/tex] are solution for our given inequality.

We have a solid dot at [tex]-3[/tex], so [tex]-3[/tex] is a solution of inequality.

We have a open dot at [tex]-1[/tex], so [tex]-1[/tex] is not a solution of inequality.

Upon combining both solutions, we will get:

[tex](-\infty,-3]\text{U}(-1,\infty)[/tex]

Therefore, the solution for the inequality is [tex](-\infty,-3]\text{U}(-1,\infty)[/tex].

An athlete eats 45g of protein per day while training. How much protein will she eat during 15 days of training?

Answers

1 gram is 1000 milligrams So 60 grams is 60,000 milligrams.

Answer:

Step-by-step explanation:

The radius of a circle is 10 cm. What is the volume?

Answers

The 3-dimensional shape of a circle is a sphere. In order to solve the volume (v) of a sphere from the radius or diameter of any circumscribed circle within is as follows:
v = 4/3 × pi × r^3, where pi roughly = 3.14
v = 4/3 × 3.14 × (10cm)^3
v = 1.33 × 3.14 × 1000cm^3
v = 4,188.56 cm^3 (cubic cm)
v = 4,189 cm^3 (rounded up)

I believe the answer is 4,188.79

Which statements are true the ordered pair (1, 2) and the system of equations?

y=−2x+4
7x−2y=3

Select each correct answer.

When (1, 2) is substituted into the first equation, the equation is true.

When (1, 2) is substituted into the first equation, the equation is false.

When (1, 2) is substituted into the second equation, the equation is true.

When (1, 2) is substituted into the second equation, the equation is false.

The ordered pair (1, 2) is not a solution to the system of linear equations.

The ordered pair (1, 2) is a solution to the system of linear equations.

Answers

this is just a matter of subbing (1,2) into ur equations to see if they make the equations true

(1,2)...x = 1 and y = 2

y = -2x + 4 7x - 2y = 3
2 = -2(1) + 4 7(1) - 2(2) = 3
2 = -2 + 4 7 - 4 = 3
2 = 2 (correct) 3 = 3 (correct)

when (1,2) is subbed into the first equation, the equation is true
when (1,2) is subbed into the 2nd equation, the equation is true
the ordered pair (1,2) is a solution to the system of equations...and it is a solution to the system because it satisfies both equations...if it would have only satisfied one of them, it would not be a solution to the system of equations

Is 6/36 and 1/6 proportional?

Answers

Yes. they are both a factor of 6

Yes, they are proportional.
6/36=1/6
Cross products is 6*6=36*1
36=36 :)

Which two graphs are graphs of polynomial functions?

Answers

a and c hope im right

It’s B and D for Plato users

The area of a rectangular piece of sheet metal is 216 ft. the width of the sheet is 6 ft less than the length what are the dimensions of th epiece of metal

Answers

just multiply lol i think

Using algebra, the dimensions of the rectangular sheet metal with an area of 216 sq ft and width being 6 ft less than the length are found to be 18 ft by 12 ft.

The area of a rectangular piece of sheet metal is given as 216 square feet, and the width is stated to be 6 feet less than the length. Use algebra to find the length (l) and the width (w) of the sheet. Since the width is 6 ft less than the length, we can express this relationship as: w=l- 6.

The area of a rectangle is calculated by the formula Area = length imes width, so we can set up the equation 216 = l imes (l - 6). Solving the quadratic equation l^2 - 6l - 216 = 0 we find that the possible values for l are 18 ft (acceptable since length is positive) and -12 ft (which is not physically meaningful for this context), leaving us with the length of the piece of metal being 18 feet. Consequently, the width would be l - 6, which is 18 - 6 = 12 ft.

Therefore, the dimensions of the piece of metal are 18 feet in length and 12 feet in width.

W far has a person traveled who ran at a rate of 5.5 miles per hour for of an hour?

Answers

Its 5.5 miles per hour so in one hour he ran 5.5 miles

Answer:

4.125 hope this helps!

Step-by-step explanation:

I know u meant 3/4 of an hour

The linear pair postulate states that if two angles form a linear pair, then they are __________ angles.

Answers

Answer: "supplementary" .
________________________________________________

Answer:

supplementary

Step-by-step explanation:

The short lines or feet at the base of type are called _______.

Answers

I believe the answer is Serifs

A movie rental website charges $5.00 per month for membership and $1.25 per movie.How many movies did Andrew rent this month if this month's bill was $16.25?

Answers

So to start subtract $5 from $16.25 for the monthly membership
That gives you $11.25
So then you Just divide...
$11.25 divided by $1.25
which gives you 9
So bill rented 9 movies for the month

Hope this helped! :)

Simplify this problem: X3 / X.

Answers

Assuming X3 means x cubed, x3/x equals x squared, with the restriction that x cannot equal 0

Hello There!

It would be x².
The question is x³/x.
X with no power is x to the power of one.
When dividing powers you subtract them.
3 - 1 = 2,
Therefore, making your answer x²

Hope This Helps You!
Good Luck :)

- Hannah ❤

Joel earns $1,700 per month. If he spends $425 on rent each month, what percent of his income does he spend on rent? A. 20% B. 331/3% C. 40% D. 25%

Answers

To get this answer, we do the part divided by the whole and multiply by 100 to get a percentage.

425 / 1700 = 0.25
0.25 x 100 = 25.

25% is your answer, letter D.

Solve the equation. How old is Sam?

Sam's age doubled plus 5 is the same as Sam's age tripled minus 1.

Question 5 options:

Sam is 6yrs old.

Sam is 4 yrs old.

Sam is 12 yrs old.

Sam is 5 yrs old.
\\
@Mochimin

Answers

6 years old. 6x2=12+5=17
6x3=18-1=17

A•2+5-3 is what I would say

The solution to -5m = -20 is negative.

True or false

Answers

m=4, false. -5*4=20.

False

a negative number times a negative number would have a positive answer

Of the birds in Monica's pet shop, 1/5 are pigeons. Of the pigeons, 1/3 are white. Look at each expression. Can it be used to find the fraction of birds in Monica's pet shop that are white pigeons?

Answers

1/15 of the birds are white

1/15.

The expression that can be used to find the fraction of birds in Monica's pet shop that are white pigeons is:

1/5 x 1/3 = 1/15

This calculation is derived by multiplying the fraction of pigeons in the pet shop (1/5) by the fraction of white pigeons among pigeons (1/3).

jasmine has $15 dollars and save $2.50 every month . radha has $0 and save $3.50 every month. jasmines savings after x months can be represented by the function f(x)=2.5x+15. radahs savings after x months can be represented by the function g(x)=3.5x after how any moths will they both have the same amount in savings? find the value of x which f(x)=g(x)

Answers

2.5x+15 = 3.5x

subtract 2.5x from each side

15 = x

they will have the same amount after 15 months

PLEASE HELP ME, I NEED IT.
Which of the following is the correct graph of the compound inequality 4p + 1 > −7 or 6p + 3 < 33?

A. a number line with open circles at negative 2 and 5 with shading in between.
B. number line with open dot at negative 2 with shading to the left and an open dot at 5 with shading to the right
C. number line with shading everywhere.
D. number line with open dot at negative 2 and a closed dot at 5 with shading in between.

Answers

The answer should be A, I do believe. I hope this helps.

The answer is B :)

I hope this helped

What could the answer be?

Answers

i don't know ???????

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